CHRONOS: Calibrated Harmonic Representation Of Norm-deviations in Observed Scenes

Problem Statement 26227 (Ministry of Defence / Smart India Hackathon)
Semantic Retrieval and Multi-Temporal Change Analysis of Satellite Imagery

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1. Executive Summary & Operational Challenge

Earth-observation (EO) archives are expanding exponentially, capturing multi-spectral, multi-temporal, and multi-sensor imagery across vast sovereign territories. Conventional catalog search relies on rigid metadata (acquisition time, sensor platform, bounding box coordinates), forcing defense and intelligence analysts to already know where and when an event occurred before inspecting pixels.

Existing automated change detection systems suffer from a fatal flaw: arbitrary pixel-difference thresholding. When an algorithm simply flags deviations in spectral reflectance, it triggers thousands of false alarms caused by:

• Seasonal phenological breathing: Crops greening, monsoons, and harvest cycles.
• Atmospheric confounding factors: Haze, thin cirrus clouds, aerosol scattering, and sensor illumination angles.
• Viewing geometry & co-registration jitter: Sub-pixel misregistration between successive satellite passes.

CHRONOS solves this challenge through a mathematically grounded, air-gapped Earth Observation Intelligence Engine. Instead of comparing isolated pairs of pixels, CHRONOS evaluates the complete trajectory of time:

1. It fits a harmonic embedding field to model natural seasonal rhythms.
2. It constructs a Difference-in-Differences (DiD) spatial cohort to cancel out regional atmospheric and illumination shifts.
3. It tracks structural anomalies through an anytime-valid Conformal Martingale E-Process, mathematically bounded by Ville's Inequality. This guarantees that the False Alarm Rate will strictly satisfy $\text{FAR} \le \alpha$ (e.g., $\le 5%$) regardless of continuous monitoring and stopping times.

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2. Core Capabilities Matrix (PS 26227 Compliance)

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3. Mathematical Architecture

3.1 Robust Harmonic Phenology Field

For any spatial tile $s$, the baseline phenological cycle across fractional year $t$ is modeled as a truncated Fourier expansion with linear trend:

$$f(t; \boldsymbol{\theta}) = \theta_0 + \theta_1 t + \sum_{k=1}^{K} \left[ \theta_{2k} \cos(k \omega t) + \theta_{2k+1} \sin(k \omega t) \right]$$

where $\omega = 2\pi$, $K = 3$ harmonics, and $\boldsymbol{\theta} \in \mathbb{R}^{2K+2}$. Parameters are solved via Iteratively Reweighted Least Squares (IRLS) with Huber loss to suppress cloud and shadow contamination. Incremental satellite acquisitions update $\boldsymbol{\theta}$ in $\mathcal{O}(d \cdot m^2)$ time using Sherman–Morrison rank-1 recursive covariance updates.

3.2 Difference-in-Differences (DiD) Cohort Normalization

To isolate local human-induced ground modifications from regional atmospheric variation, CHRONOS computes spatial cohort deviations:

$$\Delta_{DiD}(s, t) = \left( Y(s, t) - \hat{f}(s, t) \right) - \frac{1}{|\mathcal{C}(s)|} \sum_{c \in \mathcal{C}(s)} \left( Y(c, t) - \hat{f}(c, t) \right)$$

where $\mathcal{C}(s)$ is a stable cohort of nearby invariant terrain tiles. If a monsoon cloud or dust storm impacts the basin, the cohort baseline shifts equally, driving $\Delta_{DiD}(s, t) \to 0$ and eliminating the false alarm.

3.3 Anytime-Valid Conformal Martingale E-Process

To evaluate whether a sequence of residual deviations is genuine, CHRONOS evaluates non-conformity using Ledoit-Wolf shrunk Mahalanobis distances $S_t = \sqrt{\mathbf{r}_t^\top \hat{\boldsymbol{\Sigma}}^{-1} \mathbf{r}_t}$. Conformal calibration converts $S_t$ into smoothed uniform $p$-values $p_t \sim \mathcal{U}(0, 1)$ under the null hypothesis $\mathcal{H}_0$.

The test martingale (e-process) accumulates evidence across successive observations:

$$E_t = \prod_{i=1}^{t} \varsigma_\kappa(p_i), \quad \text{where } \varsigma_\kappa(p) = \kappa p^{\kappa - 1} \quad (\kappa \in (0, 1))$$

By Ville's Inequality, for any stopping time $\tau$:

$$\mathbb{P}_{\mathcal{H}0}\left( \sup{t \ge 1} E_t \ge \frac{1}{\alpha} \right) \le \alpha$$

Setting $\alpha = 0.05$ yields Ville's boundary threshold $1/\alpha = 20.0$. Even under continuous multi-year surveillance, the false alarm probability is mathematically guaranteed to remain below $5%$.

Evidence E(t)
     ^
  40 |                                  * [CONFIRMED CHANGE: Stopping Time τ]
     |                                 *
  20 |--------------------------------*----------------- Ville's Boundary (1/α = 20)
     |                               *
   5 |                  /\          *
   1 |---/\--/\--------/--\--------/-------------------- Baseline E_0 = 1.0 (Random Walk)
   0 +---|---|---|---|---|---|---|---|---|---|---> Time (Passes)
        T1  T2  T3  T4  T5  T6  T7  T8  T9  T10

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4. Repository Structure

chronoa/
├── chronos/                     # Core CHRONOS Python Library
│   ├── core/                   # Mathematical engines
│   │   ├── harmonics.py        # Truncated Fourier IRLS & Sherman-Morrison updates
│   │   ├── did.py              # Difference-in-Differences cohort normalization
│   │   ├── conformal.py        # Ledoit-Wolf covariance & conformal calibration
│   │   ├── eprocess.py         # Power-family betting martingale & Ville inequality
│   │   └── types.py            # Strictly-typed dataclasses & arrays
│   ├── engine/                 # System orchestration & retrieval
│   │   ├── query_compiler.py   # Neuro-symbolic NL -> Typed Algebra -> PostGIS SQL
│   │   ├── change_engine.py    # Mode A (Sequential) & Mode C (Bi-Temporal) pipelines
│   │   ├── discovery.py        # HDBSCAN unsupervised clustering & k-NN query
│   │   ├── field_fitter.py     # Parallel tile phenology fitting
│   │   ├── indexer.py          # Spatial tile indexing & ingestion
│   │   └── morphology.py       # Binary morphological filtering & perimeter metrics
│   ├── data/                   # Data processing & synthetic benchmarks
│   │   ├── download_real_data.py # STAC/Copernicus Sentinel-2 ingest
│   │   ├── coregistration.py   # Phase-correlation sub-pixel alignment
│   │   ├── masking.py          # SCL cloud/shadow quality mask weighting
│   │   ├── synthetic.py        # Multi-temporal benchmark generator
│   │   └── tiling.py           # MGRS / GeoTIFF window tiling
│   ├── db/                     # Data persistence & security
│   │   ├── schema.sql          # PostGIS + pgvector database DDL
│   │   ├── database.py         # SQLAlchemy & psycopg connection manager
│   │   └── audit.py            # SHA-256 tamper-evident hash chain logger
│   ├── features/               # Embedding & representation extractors
│   │   ├── physical_tier1.py   # Physical spectral indices (NDVI, NDWI, NDBI)
│   │   └── encoders_tier2.py   # RemoteCLIP & Prithvi foundation model encoders
│   └── evaluation/             # Test harness & benchmark reporter
│       ├── harness.py          # Monte Carlo false alarm & detection latency tests
│       └── report_generator.py # Markdown evaluation report generator
├── data/raw/                   # Downloaded Sentinel-2 L2A scenes (Sutlej Basin)
├── tests/                      # Comprehensive pytest test suite (48 tests)
│   ├── test_harmonics.py
│   ├── test_did.py
│   ├── test_conformal.py
│   └── test_eprocess.py
├── ui/                         # Analyst Console & Defense HUD
│   ├── api.py                  # FastAPI REST backend
│   └── frontend/               # React 19 + Vite tactical frontend
│       ├── src/
│       │   ├── App.jsx         # Command console workstation
│       │   ├── index.css       # Tactical defense design system
│       │   └── main.jsx
│       └── package.json
├── EVALUATION_REPORT.md        # Empirical validation metrics
├── PRESENTATION_SCRIPT.md      # 5-minute SIH presentation walkthrough
├── PROVENANCE.md               # Model & dataset licensing declarations
├── start_demo.ps1              # Unified one-click launch script
└── requirements.txt            # Python dependencies

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5. System Requirements & Setup

5.1 Prerequisites

• Operating System: Windows 10/11, Linux (Ubuntu 22.04+), or macOS (Apple Silicon supported).
• Python: Version 3.10 to 3.13.
• Node.js: Version 18.0 or higher.
• Geospatial Binaries (optional for production db): PostgreSQL 15+ with PostGIS and pgvector extensions.

5.2 Python Virtual Environment Setup

# 1. Create and activate a virtual environment
python -m venv .venv
.venv\Scripts\Activate.ps1

# 2. Install dependencies
pip install -r requirements.txt

5.3 Frontend Dependencies Setup

cd ui\frontend
npm install
cd ..\..

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6. Running the System

Option A: One-Click Launch Script (Recommended)

Run the automated launcher from PowerShell:

.\start_demo.ps1

This automatically boots:

• The FastAPI Intelligence Engine on http://localhost:8000
• The Tactical Analyst Console on http://localhost:5173

Option B: Manual Execution

Terminal 1 — FastAPI Intelligence Engine:

cd ui
python -m uvicorn api:app --host 0.0.0.0 --port 8000 --reload

Terminal 2 — React Defense Workstation:

cd ui\frontend
npm run dev

Navigate to http://localhost:5173 in your browser.

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7. Operational Workstation Features

The CHRONOS UI is engineered as an authentic Defense & Earth Observation Tactical Workstation, discarding generic AI chat styling for mission-critical situational awareness:

1. Target Triage & Queue:
   • Natural language neuro-symbolic query compilation (e.g., "newly built structures near a river").
   • Real-time compiler inspection showing typed algebra AST: Sem("built structures") ∧ Chg("construction") ∧ Spa(ST_DWithin, waterway=*, 500m).
   • Direct translation to PostGIS SQL pushdown filters before vector indexing.
2. Interactive Bi-Temporal Satellite Visualizer:
   • Inspect Sentinel-2 acquisitions side-by-side or in split-slider view (Pre-Event T1 vs Post-Event T2).
   • Multispectral band toggles:
     • True Color (RGB): Sentinel-2 bands B04 (Red), B03 (Green), B02 (Blue).
     • False Color Infrared (NIR): Bands B08 (NIR), B04 (Red), B03 (Green) — highlights canopy loss and structural displacement.
     • NDVI Anomaly Heatmap: Normalized difference vegetation difference mask overlay.
3. Sequential Martingale Evidence Workbench:
   • Live interactive Recharts plot of the anytime-valid e-process trajectory.
   • Dynamic Ville's Boundary adjustment slider ($\alpha = 0.01, 0.05, 0.10 \implies 1/\alpha = 100, 20, 10$).
   • Dual trace showing Harmonic seasonal model vs actual observed signal.
   • Conformal calibration $p$-value distribution and DiD cohort adjustment metrics.
4. Cryptographic SHA-256 Audit Trail:
   • Tamper-evident hash-chained ledger storing every analyst action (VERIFIED_CHANGE / FALSE_ALARM_SUPPRESSED).
   • Displays Genesis hash, Block height, Analyst ID, Timestamp, Previous Hash, and Current Hash.
   • Closed-loop conformal feedback: rejecting a candidate immediately recalibrates the nonconformity threshold.
5. Unsupervised Discovery & HDBSCAN Clusters:
   • Discovers spatial clusters of similar anomalies across the Sutlej Basin in joint $[\mathbf{v}{sem}, \mathbf{v}{phen}]$ space.
6. Air-Gapped Sovereign Telemetry:
   • Real-time monitoring of local multi-spectral Sentinel-2 GeoTIFF scenes (20 files, >3.2 GB in Sutlej River Basin) with zero internet access required.

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8. Verification & Test Suite

CHRONOS includes an exhaustive automated test suite covering exact parameter recovery, outlier resistance, martingale convergence, and false-alarm bounds:

# Run the complete test suite
python -m pytest -q

Expected output: 48 passed in ~64s (100% pass rate).

Test Suite Coverage:

• tests/test_harmonics.py: Tests design matrix creation, noise-free parameter recovery, IRLS outlier rejection (clouds/shadows), and Sherman–Morrison recursive updates ($< 10^{-6}$ error).
• tests/test_did.py: Tests synthetic cohort generation, atmospheric perturbation cancellation, and local change signal isolation.
• tests/test_conformal.py: Tests Ledoit-Wolf covariance shrinkage, Mahalanobis non-conformity scoring, empirical coverage on held-out null, and Benjamini–Yekutieli FDR control.
• tests/test_eprocess.py: Tests power betting martingale property ($\mathbb{E}[\varsigma(p)] = 1$ under $\mathcal{H}_0$), Ville's inequality bound ($\text{FAR} \le \alpha$), and persistent signal detection under $\mathcal{H}_1$.

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9. Provenance, Licensing & Air-Gapped Declaration

In compliance with Ministry of Defence requirements for sovereign operational systems (PS 26227 §2.2.7):

• 100% Air-Gapped: Runs entirely on local compute without external network requests or proprietary cloud APIs.
• Satellite Data: Sentinel-2 L2A multi-spectral rasters provided under the European Commission / ESA Copernicus Open Access Policy.
• Foundation Models: RemoteCLIP and Prithvi-EO-2.0 packaged locally under Apache 2.0.
• Codebase: Built with open-source MIT/Apache 2.0 components (FastAPI, React, Recharts, NumPy, SciPy, PostGIS).

Refer to PROVENANCE.md and EVALUATION_REPORT.md for full audit reports.

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10. Contributors & Acknowledgements

• Developed for Smart India Hackathon (SIH) — Problem Statement 26227.
• Dedicated to sovereign geospatial intelligence, verifiable change detection, and false-alarm suppression for Defense and National Remote Sensing agencies.